Optimum signal in a diffusion leaky integrate-and-fire neuronal model

An optimum signal in the Ornstein-Uhlenbeck neuronal model is determined on the basis of interspike interval data. Two criteria are proposed for this purpose. The first, the classical one, is based on searching for maxima of the slope of the frequency transfer function. The second one uses maximum of the Fisher information, which is, under certain conditions, the inverse variance of the best possible estimator. The Fisher information is further normalized with respect to the time required to make the observation on which the signal estimation is performed. Three variants of the model are investigated. Beside the basic one, we use the version obtained by inclusion of the refractory period. Finally, we investigate such a version of the model in which signal and the input parameter of the model are in a nonlinear relationship. The results show that despite qualitative similarity between the criteria, there is substantial quantitative difference. As a common feature, we found that in the Ornstein-Uhlenbeck model with increasing noise the optimum signal decreases and the coding range gets broader.     

Effect of periodic stimulus on a neuronal diffusion model with signal-dependent noise

To relate the noise intensity with a periodically modulated input signal in a single neuron stochastic model we introduce a diffusion model with both time modulated drift and diffusion coefficient. Such a model is the continuous version of a Stein model with time oscillating frequencies for the Poisson processes describing the inputs impinging on the neuron. We focus here on some aspects of the resonance phenomenon for such a model. We compare the corresponding interspike interval distribution with the analogous distribution for a model sharing the same parameter values, but with constant noise intensity. Examples with two different levels for this noise intensity are discussed. The enhancement of the height of the peaks in the interspike interval distribution appearing at the modulation period, the improvement of the phase locking behavior and an enlargement of the noise ranges where a resonance like behavior arises are the main features observed in the considered cases.     

Optimum signal in a simple neuronal model with signal-dependent noise

How does the information about a signal in neural threshold crossings depend on the noise acting upon it? Two models are explored, a binary McCulloch and Pitts (threshold exceedance) model and a model of waiting time to exceedance--a discrete-time version of interspike intervals. If noise grows linearly with the signal, we find the best identification of the signal in terms of the Fisher information is for signals that do not reach the threshold in the absence of noise. Identification attains the same precision under weak and strong signals, but the coding range decreases at both extremes of signal level. We compare the results obtained for Fisher information with those using related first and second moment measures. The maximum obtainable information is plotted as a function of the ratio of noise to signal.     

A diffusion model for population growth in random environment

The growth of a population in a randomly varying environment is modeled by replacing the Malthusian growth rate with a delta-correlated normal process. The population size is then shown to be a random process, lognormally distributed, obeying a diffusion equation of the Fokker-Planck type. The first passage time p.d.f. through any arbitrarily assigned value and the probability of absorption are derived. The asymptotic behavior of the population size is investigated.     

The random collision model and a critical assessment of diffusion and collision in mitochondrial electron transport

This review focuses on our studies over the past ten years which reveal that the mitochondrial inner membrane is a fluid-state rather than a solid-state membrane and that all membrane proteins and redox components which catalyze electron transport and ATP synthesis are in constant and independent diffusional motion. The studies reviewed represent the experimental basis for therandom collision model of electron transport. We present five fundamental postulates upon which the random collision model of mitochondrial electron transport is founded: (1) All redox components areindependent lateral diffusants; (2) Cytochromec diffuses primarily inthree dimensions; (3) Electron transport is adiffusion-coupled kinetic process; (4) Electron transport is amulticollisional, obstructed, long-range diffusional process; (5) The rates of diffusion of the redox components have a direct influence on the overall kinetic process of electron transport and can berate limiting, as indiffusion control. The experimental rationales and the results obtained in testing each of the five postulates of the random collision model are presented. In addition, we offer the basic concepts, criteria and experimental strategies that we believe are essential in considering the significance of the relationship between diffusion and electron transport. Finally, we critically explore and assess other contemporary studies on the diffusion of inner membrane components related to electron transport including studies on: rotational diffusion, immobile fractions, complex formation, dynamic aggregates, and rates of diffusion. Review of all available data confirms the random collision model and no data appear to exist that contravene it. It is concluded that mitochondrial electron transport is a diffusion-based random collision process and that diffusion has an integral and controlling affect on electron transport.     

A simple model for diffusion in independent, temporally fluctuating pores

A simple model is presented for one-dimensional diffusion in an ensemble of semi-infinite and finite pores or capillaries in which the boundary at one end of each capillary is allowed to fluctuate randomly between a perfectly reflecting barrier and a perfectly absorbing barrier. The model is independent of the spatial distribution of the capillaries; it is only assumed that there are a large number of them and that they are noninteracting. Exact solutions are possible and results are obtained, in terms of the fluctuation parameters, for the total amount per unit area of solute passed through the capillary system in the semi-infinite case, and for a permeability coefficient and time lag to steady state in the finite system. Applications of the model to diffusion in biological membranes are discussed.     

A simple macroscopic model for the diffusion and adsorption kinetics of r-adenovirus

The diffusion of viruses toward cells is a limiting step of the infection process. To be modeled correctly, this step must be evaluated in combination with the adsorption of the virus to the cell surface, which is a rapid but reversible step. In this paper, the recombinant adenovirus (rAd) diffusion and its adsorption to 293S cells in suspension were both measured and modeled. First, equilibrium experiments permitted to determine the number of receptors on the surface of 293S (R(T) = 3,500 cell(-1)) and the association constant (K(A) = 1.9 x 10(11) M(-1)) for rAd on these cells based on a simple monovalent adsorption model. Non-specific binding of the virus to the cell surface was not found to be significant. Second, total virus particle degradation rates between 5.2 x 10(-3) and 4.0 x 10(-2) min(-1) were measured at 37 degrees C in culture medium, but no significant virus degradation was observed at 4 degrees C. Third, free viral particle disappearance rates from a mixed suspension of virus and cells were measured at different virus concentrations. Experimental data were compared to a phenomenological dynamic model comprising both the diffusion and the adsorption steps. The diffusion to adsorption ratio, a fitted parameter, confirmed that the contact process of a virus with a cell is indeed diffusion controlled. However, the characteristic diffusion time constants obtained, based on a reversible adsorption model, were eightfolds smaller than those reported in the literature, based on diffusion models that assume irreversible adsorption.     

Coexistence in a simple food chain with diffusion

We show the global existence of classical positive solutions in each component of a Lotka-Volterra system with diffusion and logistic growing conditions. We are mainly interested in the search of coexistence states solving the associated elliptic problem under homogeneous Dirichlet boundary conditions.     

Optimal compliant-surface jumping: a multi-segment model of springboard standing jumps

A multi-segment model is used to investigate optimal compliant-surface jumping strategies and is applied to springboard standing jumps. The human model has four segments representing the feet, shanks, thighs, and trunk-head-arms. A rigid bar with a rotational spring on one end and a point mass on the other end (the tip) models the springboard. Board tip mass, length, and stiffness are functions of the fulcrum setting. Body segments and board tip are connected by frictionless hinge joints and are driven by joint torque actuators at the ankle, knee, and hip. One constant (maximum isometric torque) and three variable functions (of instantaneous joint angle, angular velocity, and activation level) determine each joint torque. Movement from a nearly straight motionless initial posture to jump takeoff is simulated. The objective is to find joint torque activation patterns during board contact so that jump height can be maximized. Minimum and maximum joint angles, rates of change of normalized activation levels, and contact duration are constrained. Optimal springboard jumping simulations can reasonably predict jumper vertical velocity and jump height. Qualitatively similar joint torque activation patterns are found over different fulcrum settings. Different from rigid-surface jumping where maximal activation is maintained until takeoff, joint activation decreases near takeoff in compliant-surface jumping. The fulcrum-height relations in experimental data were predicted by the models. However, lack of practice at non-preferred fulcrum settings might have caused less jump height than the models' prediction. Larger fulcrum numbers are beneficial for taller/heavier jumpers because they need more time to extend joints.     

Neuromimetic model of a neuronal filter

Experimental work in cats has shown that a series of afferent impulses from muscle receptors activated during contractions of an ankle extensor elicit declining inhibitory potentials in homonymous and synergic motoneurones. Inhibitory potentials were ascribed to the action of Ib afferents from Golgi tendon organs that are specific contraction-sensitive mechano-receptors. The decline of inhibition was, at least partly, due to presynaptic inhibition acting as a filter of tendon organ information in the spinal cord. In the present work, a computer model of the simplest spinal pathways from Ib fibres to motoneurones was designed. In order to make the model as realistic as possible, the most pertinent of the known functional properties of the neuronal elements were incorporated. Functions simulating primary afferent depolarizations of Ib terminals, i.e. the electrophysiological correlate of presynaptic inhibition, were introduced in the network. Simulations showed that declining inhibitory potentials were computed in the output stage of the network that represented the motoneurone-like element. These results support the assumption that the filtering out of Ib inputs is to a great extent due to presynaptic inhibition. The model behaved as expected, suggesting that predictions of the behaviour of neural components in the biological network should be possible upon introduction in the model of other, more complex, spinal pathways from Ib fibres to motoneurones.     

Shape effects in elastic scattering by orientationally random ensembles of simple model viruses

Recent theoretical work has shown that the complete set of polarized elastic light scattering studies should yield information about particle structure that has so far hardly been utilized. We present calculations of such light-scattering properties for a number of model structures, exploring particularly the size limit at which the new effects should become visible. The particles are assumed to be randomly oriented in aqueous suspension, and all identical to each other. We compare several particle models of differing geometrical shape, but with identical forward scattering power and identical radii of gyration. We find that one of the ten observables shows particularly desirable properties as a general large-particle characterization parameter: it is nonzero for all structures, it approaches zero as particle size decreases, and it shows an angular dependence that distinguishes among models of different shape. Assuming incident light at 350 nm, it differentiates between different shaped particles with radii of gyration as small as 50 nm. Such particles are well below the optical resolution limit and about the size of many types of viruses.     

Accuracy of neuronal interspike times calculated from a diffusion approximation

The theory of neuronal firing in Stein's model is outlined as well as the corresponding theory for a diffusion approximation which has the same first two infinitesimal moments. The diffusion approximation is derived from the discontinuous model in the limit of large input frequencies and small postsynaptic potential amplitudes. A comparison of the calculated mean interspike intervals is made for various values of the threshold for firing and various input frequencies. The diffusion approximation can underestimate the interspike interval by up to 100% or severely overestimate it, depending on the input frequencies and the threshold. A general relation between the predictions of the two models is deduced.     

Effects of deterministic and random refuge in a prey-predator model with parasite infection

Most natural ecosystem populations suffer from various infectious diseases and the resulting host-pathogen dynamics is dependent on host's characteristics. On the other hand, empirical evidences show that for most host pathogen systems, a part of the host population always forms a refuge. To study the role of refuge on the host-pathogen interaction, we study a predator-prey-pathogen model where the susceptible and the infected prey can undergo refugia of constant size to evade predator attack. The stability aspects of the model system is investigated from a local and global perspective. The study reveals that the refuge sizes for the susceptible and the infected prey are the key parameters that control possible predator extinction as well as species co-existence. Next we perform a global study of the model system using Lyapunov functions and show the existence of a global attractor. Finally we perform a stochastic extension of the basic model to study the phenomenon of random refuge arising from various intrinsic, habitat-related and environmental factors. The stochastic model is analyzed for exponential mean square stability. Numerical study of the stochastic model shows that increasing the refuge rates has a stabilizing effect on the stochastic dynamics.     

Effects of velocity jumps on blood flow in large arteries

When a human being experiences a sudden velocity change, the blood flow is disturbed. A theoretical analysis to predict the effects of sudden velocity changes on blood flow in large arteries is presented. The situations is modelled as a one-dimensional flow problem in a viscoelastic tube where the fluid viscosity convective term in the equation of motion and nonlinearity in the elastic modulus of the tube wall are neglected. The governing equations of the model are solved by Laplace transformation. The computed results show that relatively high blood pressures, capable of harming circulation, are produced even by relatively moderate velocity jumps.     

Nucleation of calcite on the sheaths of cyanobacteria using a simple diffusion cell

A method allowing observation of calcium carbonate nucleation on the sheaths of cyanobacteria and other microorganisms is described. Nucleation of calcite was obtained on the sheaths of Lyngbya aestuarii and Scy‐tonema myochrous cultures but not on Entophysalis major and Pseudanabaena minuta. Differences in the rate of nucleation were also noted in media of differing salinity.     

Analytical results on a Wilson-Cowan neuronal network modified model

Wilson-Cowan model is employed in studies concerning neuronal networks. This model consists of two nonlinear differential equations that represent the interaction between excitatory and inhibitory populations of neurons. The mutual influence of these populations is described through a sigmoidal function, which is usually chosen as the hyperbolic tangent or the logistic curve. Both choices make difficult theoretical analyses. Here we choose another sigmoidal function and analytically obtain the set of parameter values for which an asymptotically stable limit cycle exists. This result is potentially useful to analytical and numerical works on the binding problem, which is the problem of creating a coherent representation of objects from the oscillatory activity of spatially separated cortical columns.     

A simple measure of the coding efficiency of a neuronal population

We derive a simple measure for quantifying the average accuracy with which a neuronal population can represent a stimulus. This quantity, the basis set error, has three key properties: (1) it makes no assumptions about the form of the neuronal responses; (2) it depends only on their second order statistics, so although it is easy to compute, it does take noise correlations into account; (3) its magnitude has an intuitive interpretation in terms of the accuracy with which information can be extracted from the population using a simple method-"simple" meaning linear. We use the basis set error to characterize the efficacy of several types of population codes generated synthetically in a computer. In general, the basis set error typically ranks different encoding schemes in a way that is qualitatively similar to Shannon's mutual information, except when nonlinear readout methods are necessary. Because this measure is concerned with signals that can be read out easily (i.e., through linear operations), it provides a lower bound on coding accuracy relative to the computational capabilities that are accessible to a neuronal population.